What is an adequate sample size? Operationalising data saturation for theory-based interview studies

In interview studies, sample size is often justified by interviewing participants until reaching 'data saturation'. However, there is no agreed method of establishing this. We propose principles for deciding saturation in theory-based interview studies (where conceptual categories are pre-established by existing theory). First, specify a minimum sample size for initial analysis (initial analysis sample). Second, specify how many more interviews will be conducted without new ideas emerging (stopping criterion). We demonstrate these principles in two studies, based on the theory of planned behaviour, designed to identify three belief categories (Behavioural, Normative and Control), using an initial analysis sample of 10 and stopping criterion of 3. Study 1 (retrospective analysis of existing data) identified 84 shared beliefs of 14 general medical practitioners about managing patients with sore throat without prescribing antibiotics. The criterion for saturation was achieved for Normative beliefs but not for other beliefs or studywise saturation. In Study 2 (prospective analysis), 17 relatives of people with Paget's disease of the bone reported 44 shared beliefs about taking genetic testing. Studywise data saturation was achieved at interview 17. We propose specification of these principles for reporting data saturation in theory-based interview studies. The principles may be adaptable for other types of studies.